Since there is no additional information, we can assume that the given angles are respect to the horizontal axis (x), so
The answer is:
Magnitude: 95.14 lbs
Direction: 80° respect to the x-axis
Since there is no additional information about the given angles, we can assume that both angles are respect to the horizontal axis (x), positive direction to x-axis positive directions (right) and above x-axis.
100 pounds (lb) force, 50° angle:
[tex]100lbs*cos(50)=64.28lbs\\100lbs*sin(50)=76.60lbs[/tex]
50 pounds (lb) force, 160° angle:
[tex]50lbs*cos(160)=-46.98lbs\\50lbs*sin(160)=17.10lbs[/tex]
So,
For x-axis forces we have:
64.28lbs (positive direction)
-46.98lbs (negative direction)
Then,
[tex]64.28lbs-46.98lbs=17.3lbs[/tex] (positive direction)
Fox y-axis forces we have:
76.60lbs (positive direction)
17.10 lbs (positive direction)
Then,
[tex]76.60lbs + 17.10 lbs =93.7lbs[/tex] (positive direction)
So, we have the two components values of the acting force:
17.3 lbs for the x-axis and 93.7 lbs for the y-axis.
Therefore,
We have to calculate the angle between both resultant force components:
Let's calll it α
So,
[tex]\alpha=tan^{-1}(\frac{y-axisValue}{x-axisValue})=tan^{-1}(\frac{93.7}{17.3})\\\alpha=79.5=80[/tex]
Hence, the angle between both resultant force components is 80 °, meaning that the resultant force direction is positive, above the x-axis.
Now we have to calculate the magnitude of the resultant force since the sum of both resultant force components is equal to the hypotenuse of the formed triangle, we have that:
[tex]sin(\alpha)=\frac{y-axisValue}{ResultantForceMagnitude}=\frac{93.7lbs}{ResultantForceMagnitude}\\\\ResultantForceMagnitude=\frac{93.7lbs}{sin(80)}=95.14lbs[/tex]
So, we have that:
Have a nice day!
The direction and magnitude of the resultant force is 79.53° above positive x axis.
We are given with data as:
100 lbs at 50°
50 lbs at 160°
100 lbs cos(50°) = 64.3 lbs ⇒ x direction
100 lbs sin(50°) = 76.60 lbs ⇒y direction
50 lbs cos(160°) = - 46.98 lbs ⇒ negative x direction
50 lbs sin(160°) = 17.10 lbs ⇒ positive y direction
Value of x:
64.3 lbs + (-46.98 lbs) = 17.32 positive x direction
Values of y:
76.60 lbs + 17.10 lbs = 93.70 positive y direction
Now
Use Pythagorean theorem to find the resultant.
a² + b² = c²
93.70² + 17.32² = c²
8779.69 + 299.98 = c²
9079.67 = c²
√9079.67 = √c²
95.29 lbs = c
So
Resultant is 95.29 lbs.
Now
Direction of the resultant vector.
Using tan we get
Θ = tan^-1 (93.7/17.32) = 79.53° above positive x axis.
